Algebra 1
Name _______________________________
Direct and Inverse Variation Word Problems
Date _______________ Period _____
Determine whether each situation is an example of a direct variation or inverse variation. Write and equations of
variation to represent the situation and solve for the indicated information.
1)
The volume V of a gas kept at a constant temperature varies inversely with the pressure p. If
the pressure is 24 pounds per square inch, the
volume is 15 cubic feet. What will the volume be
when the pressure is 30 pounds per square inch?
2) The amount of money spent at the gas station
varies directly with the number of gallons
purchased. When 11.5 gallons of gas were
purchased the cost was $37.72. How much would
8 gallons of gas cost?
3) The time to complete a project varies inversely
with the number of employees. If 3 people can
complete the project in 7 days, how long will it
take 5 people?
4) The time needed to travel a certain distance varies
inversely with the rate of speed. If it takes 8 hours
to travel a certain distance at 36 miles per hour,
how long will it take to travel the same distance at
60 miles per hour?
5) The number of centimeters y in a linear
measurement varies directly with the number of
inches x in the measurement. Pablo's height is
152.4 centimeters or 60 inches. What is Maria's
height in centimeters if she is 64 inches tall?
6) The number of revolutions made by a tire traveling
over a fixed distance varies inversely with the
radius of the tire. A 12-inch radius tire makes 100
revolutions to travel a certain distance. How many
revolutions would a 16-inch radius tire require to
travel the same distance?
7) Karen earns $28.50 for working 6 hours. If the
amount m she earns varies with h the number of
hours she works, how much will she earn for
working 10 hours?
8) A bottle of 150 vitamins costs $5.25. If the cost
varies directly with the number of vitamins in the
bottle, what should a bottle of 250 vitamins cost?
9) For a fixed number of miles, the gas mileage of a 10) Wei received $55.35 in interest on a $1230 in her
car (miles/gallon) varies inversely with the number
bank account. If the interest varies directly with
of gallons. Stephen's truck averaged 24 miles per
the amount deposited, how much would Wei
gallon and used 750 gallons of gas in one year. If
receive for the same amount of time if she had
the next year, to drive the same number of miles,
$2000 in her account?
Stephen drove a compact car averaging 39 miles
per gallon, how many gallons of gas would he use?
11) The number of gallons g of fuel used on a trip
12) The time it takes to travel a fixed distance varies
varies directly with the number of miles m
inversely with the speed traveled. If it takes Pam
traveled. If a trip of 270 miles required 12 gallons
40 minutes to bike to her fishing spot at 9 miles
of fuel, how many gallons are required for a trip of
per hour, how long will it take her if she rides at 12
400 miles?
miles per hour?
13) The time needed to paint a fence varies directly
with the length of the fence. If it takes 5 hours to
paint 200 feet of fence, how long will it take to
paint 500 feet of fence?
14) The number of bricks laid varies directly with the
amount of time spent. If 45 bricks are laid in 65
minutes, how much time would it take to lay 500
bricks?
15) The time to prepare a field for planting is inversely 16) An egg is dropped from the roof of a building. The
proportional to the number of people who are
distance it falls varies directly with the square of
working. A large field can be prepared by 5
the time it falls. If it takes 0.5 second for the egg to
workers in 24 days. In order to finish the field
fall 8 feet, how long will it take the egg to fall 200
sooner, the farmer plans to hire additional workers.
feet?
How many workers are needed to finish the field
in 15 days?
17) The number of hours needed to assemble
computers varies directly with the number of
computers. If 12 computers can be assembled in 9
hours, how many computers can be assembled in
15 hours?
18) The weight of a person varies inversely as the
square of the distance from the center of the earth.
If the radius of the earth is 4000 miles, how much
would a 180 pound person weigh 2000 miles
above the surface of the earth?
19) Bob's dentist determined the number of cavities
20) To balance a seesaw, the distance, d (in feet), a
developed in his patient's mouth each year is
person is from the fulcrum is inversely
inversely proportional to the total number of
proportional to his or her weight, w (in pounds).
minutes spent brushing during each session. If Bob
Roger, who weighs 120 pounds, is sitting 6 feet
developed 4 cavities during the year in which he
away from the fulcrum. Eva weighs 108 pounds.
spent only 30 seconds brushing his teeth each time,
How far from the fulcrum must she sit to balance
how many annual cavities will Bob develop if he
the seesaw?
increases his brushing time to 2 minutes per
session?